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## 7.3 Chapter summary (ESBP3)

Presentation: 23WS

• The kinetic theory of gases helps to explain the behaviour of gases under different conditions.

• The kinetic theory of gases states that gases are made up of constantly moving particles that have attractive forces between them.

• The pressure of a gas is a measure of the number of collisions of the gas particles with each other and with the sides of the container that they are in.

• The temperature of a substance is a measure of the average kinetic energy of the particles.

• An ideal gas has identical particles of zero volume, with no intermolecular forces between the particles. The atoms or molecules in an ideal gas move at the same speed.

• A real gas behaves like an ideal gas, except at high pressures and low temperatures. At low temperatures, the forces between molecules become significant and the gas will liquefy. At high pressures, the volume of the particles becomes significant.

• Boyle's law states that the pressure of a fixed quantity of gas is inversely proportional to the volume it occupies so long as the temperature remains constant. In other words, $$pV = k$$ or:

$p_{1}V_{1} = p_{2}V_{2}$
• Charles' law states that the volume of an enclosed sample of gas is directly proportional to its Kelvin temperature provided the pressure and amount of gas remains constant. In other words, $$\frac{V}{T} = k$$ or:

$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$
• The pressure of a fixed mass of gas is directly proportional to its temperature, if the volume is constant. In other words, $$\frac{p}{T} = k$$ or:

$\frac{p_{1}}{T_{1}} = \frac{p_{2}}{T_{2}}$
• For Charles' law and for the pressure-temperature relation the temperature must be written in Kelvin. Temperature in degrees Celsius ($$\text{℃}$$) can be converted to temperature in Kelvin ($$\text{K}$$) using the following equation:

$T_{K} = T_{C} + \text{273}$
• Combining Boyle's law and the relationship between the temperature and pressure of a gas, gives the general gas equation, which applies as long as the amount of gas remains constant. The general gas equation is $$\frac{pV}{T} = k$$, or:

$\frac{p_{1}V_{1}}{T_{1}} = \frac{p_{2}V_{2}}{T_{2}}$
• Avogadro's law states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules.

• The universal gas constant (R) is $$\text{8,314}$$ $$\text{J·K^{-1}·mol^{-1}}$$. This constant is found by calculating $$\frac{pV}{T}$$ for $$\text{1}$$ $$\text{mol}$$ of any gas.

• Extending the above calculation to apply to any number of moles of gas gives the ideal gas equation:

$pV = nRT$

In this equation, SI units must be used. The SI unit for volume is $$\text{m^{3}}$$, for pressure it is $$\text{Pa}$$ and for temperature it is $$\text{K}$$.

 Physical Quantities Quantity Unit name Unit symbol Moles ($$n$$) moles $$\text{mol}$$ Pressure ($$p$$) pascals $$\text{Pa}$$ Temperature ($$T$$) kelvin $$\text{K}$$ Volume ($$V$$) meters cubed $$\text{m^{3}}$$
Table 7.2: Units used in ideal gases